The Biggest Ideas in the Universe | 7. Quantum Mechanics

The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody.
This is Idea #7, "Quantum Mechanics." We talk about the quantum recipe -- the basic ingredients of wave function and Schrödinger equation, and how they are mixed together -- leaving deeper interpretational issues for later.
My web page: www.preposterousuniverse.com/
My KZbin channel: / seancarroll
Mindscape podcast: www.preposterousuniverse.com/p...
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Blog posts for the series: www.preposterousuniverse.com/b...
Background image: woowpaper.blogspot.com/2020/0...
#science #physics #ideas #universe #learning #cosmology #philosophy #quantum

[@Baskerville175]

It is such a pleasure to listen to someone who is so expert in his field and communicates so well

[@houstonsaft]

You are now one of my favorite humans for doing this.

[@j82man10]

🦁

[@MartinWilson1]

You can tell by the comments that Sean has reached a Feynman-level of teaching and inspiring. These videos will be referred to time and time again. We are watching history in the making. Despite them being lectures about 'we don't know', The honesty he provides us laymen trumps the deception laid on undergraduates. Devoting his career to turning this big ship around, in order to save future generations going wildly off-course. Cheers Sean.

[@MartinWilson1]

Heh, with hindsight, agreed.

[@imasiontist653]

While I see the Feynman comparison (of course I wasn't alive during that time but I have watched videos of him), I'm not sure what you mean about "the deception laid on undergraduates", or by "turning this big ship around".

[@MartinWilson1]

I'm a Siontist Keep watching, all will be explained by Sean in the coming videos. He explains in his books and videos on the great courses how undergraduates have been cheated into just accepting the Copenhagen interpretation, which is clearly wrong. Keep watching, it's gonna be an interesting ride for those that don't know why he advocates the many worlds theory.

[@obsoleteboomermobileobsole2043]

I think Sean will likely be responsible for a change of perspective in QM after an entire generation of physicists grow up watching his videos

[@grow-nannyinc1444]

For me its Feynman, Sean Carrol then Dirac in that order. He's certainly a living legend. Im a huge fan of amazing teachers. Feynman was so great because of his teaching style. Sean inpired me though. I love that his mind is always of the cusp of the greatest new ideas! He's one of 5 people alive I would love to meet!

[@squatchymcsquatchsquatch3015]

You literally have no idea how much I appreciate that you're putting this out during this period of time, and how much I enjoy being able to follow along with it. I love that you show how calculus is integral (pun intended) to all of these ideas and show a few examples, but that your focus is on the ideas themselves, not trying to explain 5d tensor homework problems to people like me who C'd my way through calc 106 the second time through... That's how you get people EXCITED about these big ideas. I am excited, because you sir, are doing an amazing job! Thank you.

[@dozog]

Dr Carrol had a very wide spread wavefunction for your appreciation. But it totally collapsed now. 🤔

[@deansundquist9601]

Squatchy McSquatchsquatch +1

[@MegaTrevor04]

Was about to post something along the same lines then read the first comment and was happy to see I wasn't alone

[@thesciencechannelwithnocon9329]

Love it keeep up gooooooooooooood work!

[@Jay-xh9dl]

Well said! and same!

[@jamesbra4410]

The only thing better than free physics lectures is physics lectures from the master, Sean Carroll, himself. Great day! Perhaps if this pandemic produces anything positive, it is a new Isaac Newton with all the answers lol.

[@ghoulunathics]

we are honored to have a man like you having his own youtube channel.

[@roblindsey-nassif4433]

It's a privilege to hear Sean Carroll. He's brilliant yet down-to-earth. What a thrill.

[@2945antonio]

Out of laymen's curiosity I watched your Lecture #7, Quantum Mechanics (and propose to watch a few more of interest to me) and found it fascinating, even if a whole of the material went over my head. I wanted to tell you how very nice of you it is to devote your time and effort to make physics (some aspects of it) available to ordinary members of the public. Thank you very much for your generous offer of time and expertise.

[@philochristos]

I couldn't agree more with what you said at the end of this video about understanding reality vs. making predictions. It's refreshing to hear you say that.

[@Ramino171]

With that level of simplicity and elaquency, this presentation can as well be given in the kindergartens. Great job!

[@dmfrench]

You wouldn't know what I love about Dr. Carroll? He's not perfect, and he doesn't try to hide it. I always thought such a great mind would be superhuman, but not so! He gives me hope.

[@ArvinAsh]

Fantastic video that summarizes not only what QM is all about, but also how it came about. Brilliant! Should be required viewing for any student of quantum mechanics.

[@bahauddinalam4109]

You're also here sir!!!😄

[@SonuSingh-sn8qg]

I love these guys. Arvin you have become one of my favorites

[@andybeans5790]

I'm not falling for that "You can watch cloud chambers..." trick again, I lost a whole day looking at tracks from all sorts of particles, totally mind-blown.

[@grow-nannyinc1444]

I've been following you since your talks on quintessence and ive listened to 'The Big Picture' and 'Something Deeply Hidden' at least 50x each. Thanks for being my mentor all these years.

[@thesciencechannelwithnocon9329]

so glad your watching him isn’t this quantum physics AWESOME!?

[@grow-nannyinc1444]

@@thesciencechannelwithnocon9329 its my favorite! I also study botany, electronics engineering and software programming but almost every night Sean Carrol helps my mind stop spinning and lets my imagination run wild! Perfect for bed time!

[@akumar7366]

Oh my God this is the hardest thing ever concept for the layman to understand, hopefully my limited understanding will be improved, Thank you Sir.

[@matiasreinoso3393]

He literally explained most of whats in your intro modern physics course at Uni in an hour

[@omarino99]

I would say relativity is harder to understand but that’s just my take

[@thesciencechannelwithnocon9329]

Think of it as a brain.. One part another part and it keeps going almost forever till nerves end that should make you understand if it made you more confused contact me and reply to my comment

[@YogiMcCaw]

As someone who can't do a lot of the math (but i could follow the simplified equations you drew), these lectures are clarifying a lot of concepts that I had only vague knowledge of. Of course, I still only have a beginner/novice knowledge of the these ideas, but nevertheless, this is helping me clarify how i think about these concepts that people bat around a lot when they talk about QM. Thanks, Sean!

[@isabelab6851]

Still trying to get my head around this! I wish I spent more time think about this in my youth. Thank for expanding my universe

[@thesciencechannelwithnocon9329]

Take ur time m’am Just chill and think about how far this technology and mind goes

[@wimbrinkman5747]

Isabel AB🍈🥥🍊

[@scienceexplains302]

No point in regretting, just go for it now. I am older than you are and am probably at about the same level of understanding

[@thingsiplay]

12:24 "We have ultraviolet, which is even bluer than blue." - Sean Caroll, 2020

[@YogiMcCaw]

There's a song in there somewhere...

[@ToriKo_]

@@YogiMcCaw She left me during the deep of Winter, there was nothing I could do... Her name was Ultraviolet, and she left me bluer than the deepest blue..

[@weissmann7770]

great kudos to you for using your time to put out these "classes" - super good presentations - clear and concise and at the right speed and depth

[@kayrosis5523]

That I could generally (though not perfectly) follow along with this just by listening, and not even watching is a testament to how well you're translating this into terms laymen can understand. This is a fantastic series you're doing Mr Carroll, I'm sure countless people will turn to these in the coming years.

[@steliosp1770]

Not only is Dr Caroll releasing great content but it just keeps and keeps on coming. I love it :D Thank you once again Dr Caroll.

[@KieranGarland]

Would still really love a primer on the classical ideas of electro-magnetism and statistical mechanics. Have never developed a strong enough intuition for either of them. That said, this is great episode in the series. Thanks again for sharing these, they're really so useful and so enjoyable.

[@OGZxBEEf]

I haven't felt this inspired to continue pursuing an interest in such a long time. Having even a somewhat clear idea of where the line is drawn between what we do know and what we don't is such a motivating sensation.

[@thesciencechannelwithnocon9329]

Same Here wow never met somone with the same feeling as me!

[@jeffwells1255]

What a great video! You clarify so many things that I was fuzzy about all along and I only wish you were there when I was ploughing through this stuff 50 years ago! You also touched on the difference between "observation" and "measurement," something that I wish scientists had done from the beginning, because to the uninitiated an "observation" implies an "observer," and that implies a conscious mind to a lot of people. This has led to travesties like Deepak Chopra telling people that "they create the universe" but simply looking at it, which is of course barking nonsense. I wish science could change its terminology and change observation to measurement, but it's probably too late for that. In the same vein, the use of "theory" to label what is actually an "explanation" of a set of related facts has resulted in encouraging millions of ignorant religious types to insist that scientists are only guessing about these things. I look forward to more of these videos!

[@johnp1]

Best introduction to QM I've seen so far.

[@anitathorsteinsson3575]

Thank you so much for doing these Sean. I only did maths and science until year 10, because I never really understood the point. In my maths classes, there was usually an utterly bored teacher who would scratch his balls while staring out the window and pointing to the blackboard. I had no idea what the point of learning any of it really was. There were some numbers and some letters and some angles and apparently I was going to need this for when I did a spot of carpentry or needed to pay for things. Meanwhile I drew pictures of bunnies and people on a notepad and waited impatiently for my art class, or for the time when I never had to do any of that useless crap again. Meanwhile I had some unrelated questions about the universe that I thought about constantly. For example, how is this all put together? What is all this stuff, how does it all get made, what is reality? How on earth do people figure out how far away planets are, what is in their atmosphere? And then on a smaller scale, what the hell is a wave function and a Hamiltonian and how on earth can something only really ping into a definite existence and location when measured? I wanted to know the answers to all of these questions. It turned out these were related to maths and science after all. I can’t help thinking how much more I could have known about the universe by now if someone had explained some things to me, like what the real purpose of maths and science was. But no-one did, and there was no KZbin in the early 90’s. This is where you come in. I can’t even begin to explain how clearly you have explained what was previously inaccessible to my brain. Everyone says to me that I have to start from the beginning and learn the basics and then go from there. But my brain works in the opposite direction. I want to know the answers to the big questions and then work backwards to understand what it all means and how someone worked this out. Obviously I can’t do any of the calculations but I now understand that it’s not the numbers and the letters which are the point, but what the letters actually represent. I didn’t even understand that. Now when you’re writing a calculation on your board I’m thinking, I know what you mean when you’re saying that. I understand why it is that things are kind of nowhere until we pin things down by measuring them. It just is that way and it’s bloody amazing. I now understand so much more about the universe and how people figured it out. So, thanks. I really appreciate all your efforts. You are a kick-ass teacher.

[@LoganHudak]

Sean, you’re the best. Thanks for doing these videos- appreciated.

[@ARreckless14]

Love this stuff Sean! And you explain it so innately and in a way that’s relatable and comprehensible. Thank you sir!

[@nilshellblom2629]

What an age to be alive in when knowledge like this is accessible like this

[@antoninbesse795]

There were several possible observational outcomes before watching this series. I know know that it’s truly excellent. Thank you for sharing your knowledge so generously and comprehensibly.

[@kamiodd2873]

Amazing series of lectures :). This feels like the adult version of the weekly shows (Star Trek with my grandpa) we were waiting for when we were kids :). Can't wait to see the next video! Many thanks for these inspirations!

[@larsalfredhenrikstahlin8012]

Thank you so much for this! You're an astoundingly good teacher

[@GasSnake101]

I accidentally put your audio book on shuffle and it made more sense.

[@griffics6080]

I'm loving these videos - thanks so much for making them.

[@derekaegerter9172]

Thanks, Dr Carroll, for doing these! I loved From Eternity to Here and listened to it on several long lonesome road trips to and from university.

[@zeynoleee]

It's extremely infuriating to come across videos like this, now that I graduated from high school. I can see how a waste of time my physics classes were compared to this. My teachers had either no real understanding of the topic or teaching in general. It's oftentimes forgotten how important it is to set the context before delving into subjects that are new and foreign to our understanding of the world we live in. And this is just a brilliant example of a high school level introduction of a subject!! thanks:)

[@donegal79]

wow, you sound bitter. You know you weren't ready at 16 - 17 for this. Not really. No you weren't. Nope. You might thing you were, but no. This was just a philosophy lesson.

[@berserker8884]

@@donegal79 Except that people start programming when they are 10 and programming immediately requires more logical and abstract thinking than any of these videos, because you are doing the actual hard work within pure mathematics. If you are doing the actual physics, then it is just as difficult as anything, but these videos are definitely a very clear and nice introduction to the basic physics.

[@dankuchar6821]

Having taught High School, I can feel your pain. The issue is that there are so many people in class, all on different levels, that there simply isn't enough time to cover things in detail. We are required to cover so much material that we cannot spend the time needed to really get into the subject. And, the math required is far beyond High School students. One on one, with the few students that care, it's wonderful to be able to explain things in sufficient detail.

[@pseudocalm]

High school physics almost never gets much beyond Newton anyway. It starts at the same point Sean started in episode 1. The reason we still start there today is the same reason we have been able to build our understanding up to quantum mechanics in the first place.

[@neruneri]

@Carbon Josh G The issue is that while some absolutely could process this at 17, you can't reasonably expect the general school population to do so. Individuals are sadly not the optimal thing to focus the teaching level on, not even the entire classroom is, you focus it on literally all the classrooms at the same level, simultaneously. It's incredibly difficult to balance teaching difficult topics and making sure they are useful to have been taught to the broad population.

[@paulperkins1615]

Watching this, find myself picturing Classical Mechanics as a kind of lost Eden from which physicists have been expelled, but always long for.

[@swoop8047]

Thank you for these wonderful layman sessions!

[@dontpresstheredbutton9962]

Wonderful to have such free access to your mind with all your videos Sean. Extraordinarily generous.

[@etienga]

Fantastic. This has all of a sudden become so intuitive. Sean I need to shake you hand.

[@spiffylongstockings]

These videos are so great. Thank you so much for making these.

[@blcenglish]

Brilliant and truly inspirational lectures. You have an amazing talent for explaining complex ideas simply. I love how you put the maths to one side to facilitate a deeper understanding of concepts and clarify what the maths is actually describing.

[@serkantopcu5432]

Dear Sean carrol I would like to thank you for sharing your knowledge. The way you explain everything is super . I hope you keep going on like this

[@edwardlee2794]

To conclude before it is going to conclude that Dr. (Dear) Sean Carroll should be awarded the Nobel prize in physics for popularizing physics (just like Paul A. Samuelson for economics) . The minimum impact will be the potential of whole new generation of future Nobel candidates. Thanks (Dr.)

[@TheAlchemistZero1]

Phenomenal episode, greatly appreciated.

[@PaulSebastianM]

Only 116k subscribers shows why I never had or seen teachers this good in school.

[@Shonucic]

These videos are so great, thanks again for creating this series!

[@xyzzy4567]

Awesome video, thanks! I really appreciate when Sean distinguishes what is know from what is theorized. It’s frustrating when other videos on quantum mechanics state everything as absolute fact when in reality, physicists are trying to workout some of the finer details. Looking forward to the next video.

[@fabiocaetanofigueiredo1353]

SPECTACULAR. Thanks Prof. Carroll 👏

[@venil82]

Who's disliking this? Must be Newton

[@DEATH0RI0N]

Epic.

[@gwills9337]

So good, i hope Sean reads your comment

[@larsalfredhenrikstahlin8012]

Copenhagen-fundamentalists

[@venil82]

@Astute Cingulus if you're watching these series, you should know there's no god 😅

[@jacobm5167]

The electric universe crowd and the flat Earthers.

[@gbye007]

Brilliant. This has never been done before with such a balance between some symbolism (maths) and 'understanding'.

[@thom1218]

Glad to see you're embracing youtube's video format to deliver great content beyond the podcast format!

[@simos11]

Exceptional video! Thank you for all this effort and keep doing such works!

[@abhinavanand937]

I would never understand quantum mechanics in classes and would always remember the formulas. However the video tutorial and the book “ something deeply hidden ‘ present a robust combination in understanding the intriguing subject.I am watching the video first and the book will be next. Thank you Sean Carroll for bringing up these amazing ideas in such subtleties without losing the essence. Ever grateful 🙏

[@troytunello3200]

I really appreciate the way you explain things. Keep it up!

[@Bazzo61]

I so wish I'd had you Sean as my Physics teacher at university. Yes, these topics were covered in my undergradute course but your explanations are so much clearer. I finally understand Heisenburg's uncertainty principle - thank you :-)

[@N7_CommanderShepard]

I’m taking my formal course in quantum mechanics this fall, this was a great overview of what I learned in modern physics. Thanks for the review Dr. Carroll!

[@charlesmurray1491]

Prof Carroll, fantastic videos!!! I, for one, really appreciate that you cannot talk and write at the same time. The pauses give me a little time to get my head around what you are talking about.

[@kiritdave4207]

Superb explanation. the best ever heard! thank you, Sir. Answered so many of my doubts that had bothered me for so long.

[@celestialaeonproject]

Thank you for this

[@lambda4931]

Fantastic stuff! Feel honored to hear it.

[@thomassaurus]

This video is answering questions about quantum mechanics that I've been looking for for awhile, especially near the end of the video.

[@jimkane7162]

How privileged are we that we can watch quantum mechanics lectures from Sean Carroll for free!

[@jimkane7162]

@Dirk Knight Okay Stephan Hawking

[@steveseamans9048]

Sean, so good! I wish I was back in school. Seems like this subject really pushes your buttons more than other videos you’ve done. I really liked your podcast with David Albert. I think you’re zeroing in some real understanding.

[@user-zr7iq6xr6m]

Thank you, Sean Carroll , for taking us back to the basics! 🙂

[@drazenbuljovcic9478]

Sir, so much respect for your work! Love the creative idea for videos!

[@sebastianclarke2441]

I can't thank you enough for how much you've contributed towards keeping so many of your students focused through these uncertain times. I offer my immense gratitude for all your hard work throughout this crisis!! Here are a few wave function questions I would like to offer up: Can a wave function be collapsed by another wave function/virtual particle or must it be an actual particle? Does the wave function extend across all of the splitting many worlds born from wave collapse and all the bubble-verses born from inflation? Is it correct to think that there is only one wave function and that no single part of it can ever fully collapse? Is time reversed matter expected to merge diverged wave functions? Would it be correct to think that the most collapsed "part" of the wave function would be the matter furthest away from us in time?

[@marijica]

Omg thank you sir! I never understood the wave function until now

[@katherinetempleton1360]

Wonderful video!! You have an amazing ability to make very complex subject matter understandable to the average person. Thank you!

[@kagannasuhbeyoglu]

Thanks a lot for lectures Mr. Sean Caroll.

[@dr.mouserslessons4846]

This is great stuff. Thank you for your time

[@johnpetkos5686]

"Something Deeply Hidden" is an amazing book written by an amazing human being.

[@LA6UOA]

You are my hero! Thank you, Sean!

[@savage22bolt32]

From 46:00 to 47:00 was the clearest animation of the collapse of the wave function. I'm still not sold on the idea, but now I have a visualization of it. Thank you for that!

[@SandipChitale]

Sean, can you please clarify definitively that even in Copenhagen interpretation whether or not the “observer” or “measurement device” in a quantum experiment, does or does not have to be a conscious entity like a human. As I understand it, “observer” is simply a macroscopic thing that interacts with a quantum system - which causes the “collapse” of the wave function according to Copenhagen interpretation. Did any one of Copenhagen club members ever say that “observer” has to be a conscious entity? I know that Jon Von Neumann and Wigner proposed that “observer” has to be a “conscious” entity. But later Wigner changed his mind. How many modern scientists use the word “observer” to mean “conscious” entity? Could you please convince your fellow scientists to clarify the word “observer” as it is used in quantum mechanics. IMO the use of the English word - observer - for the measuring device in quantum experiments, was a unfortunate choice and has caused countless amount of mischief by new age gurus like Deepak Chopra. I am really annoyed by it. I am surprised that even at respectable conferences like FQXi there is a discussion about “observer” in quantum mechanics as if it needs to be a conscious entity. Or is it still true many scientist think that “observer” has to be a conscious entity? It is obviously true that a macroscopic conscious entity can play a role of “observer” not because it is it is conscious but because it is macroscopic.

[@pb4520]

Thank you so much for trying to help us understand. I appreciate these so much.

[@wally_g5192]

Fabulous discussion! Thank you so much!

[@cmacmenow]

Lovin' the MW backdrop!

[@integerdivision]

As someone who is not a fan of Copenhagen (easy but utterly magical) nor Many Worlds (elegant but revolting†), I’ve wandered through other theories with similar disappointment (insofar as a CS person can understand the mathematics - I’m workin’ on it). Watching this made a lightbulb go off in my head that is probably nothing, but having never encountered it elsewhere, why not share it ¯\_(ツ)_/¯ Hopefully it contributes to the conversation in an interesting way even if flawed… Some assumptions regarding place: • Everything is made out of energy • Energy is the vibration of fields • These vibrations move according to their wave function and nothing else • All wave functions adhere to the principle of least effort†† • The principle of least effort is the action with the smallest energy expenditure • The smallest expediture means that energies out of phase with each other will destructively interfere while those in phase will constructively interfere • Therefore, the wave function of a packet of energy is influenced by the wave functions of other packets of energy creating wave functions _for their interaction_ • These interactions themselves may appear as packets of energy, absorbing or otherwise transforming the originals in quantized amounts • The wave function of a system is the sum of all the wave functions of individual energy packets _and_ their interactions _and_ their interactions’ interactions ad nauseum Some assumptions regarding time: • There is a smallest time in which something can change • Everything has a smallest time, say a click of a clock • A clock is one cycle of vibration, an overtone of a fundamental click (an integer multiple greater than one of a click) • Any clock faster than two clicks will appear slower because of aliasing (Nyquist frequency) • This gives us a maximum on the amount of energy something can have • Clicks of clocks are always out of sync initially • It takes effort to keep clicks out of sync so they will eventually sync up • The clock of the interaction of two clocks is the least distance between them • Synchronized clicks are quantized - discrete • Unsynchronized clicks can be any arbitrarily small amount out of sync with each other - continuous Maybe I have gone far afield with the above, but taking them as true, some observations: • All wave functions must be approximations • Despite the discrete nature of quanta, their interactions are continuous when accounting for their phase relationship • This continuity leads to even trivially simple systems acting chaotically (the three-body problem) • Quanta follow the path of least effort through this continuous interference which includes interference with its own interactions • The result we observe is the wave function of these recursively chaotic interactions which is typically a well-defined corpuscle • The artifacts of our necessarily incomplete knowledge of the system make the outcome appear random • Randomness is just the shadow of infinity, in this case of countably many interactions of uncountably many possible ones • Trying to wring out infinity leads us to create wave function collapse or hidden variables or many worlds As far as I can tell, this is not any observer-dependent interpretation. There are no hidden variables even if aspects of the system are unknowable enough to make it chaotic. It doesn’t require a spontaneous collapse. The power stack of interactions doesn’t seem any more farfetched than anything else in QM. I don’t know if this is what I think, but after an evening, it feels kind of nice. Please poke holes. † Revolting in the sense that first thing I thought of were all the terrible things that I didn’t do but had a non-zero probability _certainly happened_. It is literally the most revolting thing. I have come to accept it, but just like death, I’d rather not †† I prefer _effort_ to _action_ because a greater action may require less effort, as in the case of sympathetic vibration

[@LeonVanDyk]

Brilliantly helpful. Thanks Sean.

[@pizzacrusher4632]

Another fantastic, well delivered, fascinating Idea. Thank you!! (as an aside I was hoping double slit experiment would come up, since I've been waiting my whole life to ask a question about it...)

[@Sad_King_Billy]

Just finished Something Deeply Hidden and came to youtube to do more research. Happy to see you have this video!

[@juanr859]

Beyond fantastic work !!!…. I truly appreciate your awesome teaching talent. I am very grateful for your proactive, professional disposition to share your knowledge. I am forever grateful

[@Dr10Jeeps]

Excellent! I could listen to Dr. Carroll for hours. Oh, wait, I already do.

[@CleerPond]

Mesmerized; Had attended four graduate schools in engineering, your explanations here is among the best one hour I spent in a lecture. Bravo Sir!

[@BurkeLCH]

THANK YOU FOR THE UPLOAD! :D

[@CorezMon]

It never ceases to amaze me how much we know and in that how much we do not.

[@calinwerlein1378]

A huge gift for society to have people like you. Please keep it up

[@SicilianDefence]

You are awesome! These videos are my daily joy 😊

[@tn324]

Such a good explanation, love it Sean

[@dansatMaryland]

Meteorologists do maths but we do not get into quantum mechanics, so I really appreciate this!

[@davidhughes6]

Great Summary-Loved it! I agree completely with your point on reality. The wave function does describe the real universe and we should all agree on that. Fascinating stuff!!!

[@lampkowski]

Absolutely great lecture, for some reason it let me understand things I've new about but I didn't understand them :) cheers Mate

[@pjosip]

Thank you for this explanation!

[@appercumstock3017]

Fantastic! ThX a lot Prof. Carroll!!

[@davidsardarov252]

wonderfull person most people of today are missing to hear. You are awesome!

[@kaikunymous4687]

I learned something about quantum mechanics. This is amazing!

[@klasnm_5364]

Thanks for sharing, mr Carroll.

[@Dr10Jeeps]

Here I sit on August 29. 2020 knowing that Dr. Carroll has already given his last session in this series. What a pity for they have been extremely informative and enjoyable.

[@georgekomarov4140]

I'm a mathematician, I know what Hilbert space is and how to solve partial differential equations and so on. But this is the first lecture ever that finally made me _understand_ what wave function, Heisenberg principle etc. really _mean_. Thank you so much. It's a shame your videos aren't getting as many views as they deserve, they're very underappreciated.